Probing the Universe with a Relativistic Light Sail or Einstein-Dirac Fermions

Résumé

Humanity’s undeniable and profound curiosity about the cosmos drives it to develop both direct and indirect probing strategies: direct exploration through physical visits using probes, and indirect exploration by observing cosmic electromagnetic field, gravitational waves, and particles such as fermions.

Building on these two strategies, this thesis proposes two distinct approaches to probing the Universe.

In the first approach, we present a relativistic kinematic and dynamic model of light sails with arbitrary reflectivity and absorptance, undergoing non-rectilinear motion as a method of interstellar exploration. The problem involves solving for the trajectory of the sail in 4-dimensional Minkowski spacetime
manifold. By detailed computation, we derive the worldline of the sail in the laser’s frame in the sail’s proper time.

The second approach applies the Two-State Vector Formalism and weak measurements within a spatially homogeneous and isotropic cosmological framework to Dirac spinors coupled to classical gravity. We compute weak values of the energy-momentum tensor, the Z-component of spin, and pure states. Extending the work of Finster and Hainzl on Einstein-Dirac cosmology, we demonstrate that the Universe’s accelerated expansion can be interpreted as a consequence of postselection. We show also that weak measurements can amplify signals with simpler equipment by carefully selecting initial and final
state vectors. Furthermore, this process reveals geometric properties of the spacelike three-manifold of the Cosmos, opening new way on probing the structure of the Universe.

Additionaly, we explore the mathematical framework underlying the Dirac equation beyond the standard dimension and signature. This enterprise reveals its symmetric rich properties and aesthetic diagrammatic representation.

la date de réponse	31 mars 2025
langue originale	Anglais
L'institution diplômante	Universite de Namur
Superviseur	Andre Fuzfa (Promoteur), Dominique Lambert (Copromoteur), Yves Caudano (Président), Jérémy Rekier (Jury) & Félix Finster (Jury)